Data

Maths Learning Centre

University of Adelaide

Semester 1 2023

APPROACHES TO CULTURE

Please have a look at the cards on the table �and talk with others about what you notice.

Main points

• The Maths Learning Centre are friendly people to talk with
• Data helps you see patterns you can’t see yourself, �and helps you unsee patterns you thought you could see
• You need your understanding of context and story to make sense of data
• Data terminology to make it easier to talk about data
• The data terminology “significant” has a very specific meaning which is not the same as important.

Maths Learning Centre

• Safe place to talk about anything mathematical related to any course.
• No maths is more or less worthy to discuss
• 10am to 4pm, Monday to Friday
• Level 3 Hub Central, or via Zoom
• www.adelaide.edu.au/mathslearning

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ACTIVITY

The cards show information about the 52 Disney theatrical release animated feature films (which have a single story) up to 2022.

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What do you notice?

Terminology

• SUBJECT: �Whatever things you write information down about�eg: Disney films
• VARIABLE: �A specific type of information you write down�eg: Running time, Australian rating
• CATEGORICAL VARIABLE: �A variable whose options for each subject are categories�eg: Australian rating, Month
• NUMERICAL VARIABLE: �A variable whose options for each subject are single numbers�eg: Running time, Number of songs sung by characters

ACTIVITY

Think of some new variables you could write down about these subjects. Decide if they’re categorical or numerical.

ACTIVITY

Organise the cards to investigate the month in which a Disney film was released.

Terminology

• BAR CHART: A chart that shows how many or what percentage of subjects are in each category.

ACTIVITY

Organise the cards to investigate the running time of Disney films.

Terminology

• HISTOGRAM: Like a bar chart, but the categories are ranges of possible numbers from a numerical variable.
• BINWIDTH: How wide the bars are on a histogram.

Terminology

• DISTRIBUTION: A description of how likely subjects are to have the various possible numbers in a numerical variable.
• SKEWED: A distribution is skewed when subjects are more spread out at one end compared to the other. It’s skewed positively when the bigger end is more spread out; it’s skewed negatively the smaller end is more spread out.

ACTIVITY

Make two separate histograms of running time, �one for G films and one for PG films.

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What can you say about the relationship between rating and running time?

ACTIVITY

Terminology

MEDIAN: The number that has half the subjects before it and half the subjects after it.

MEAN: The number that each subject would have if you found the total and shared it evenly among all the subjects.

STANDARD DEVIATION: A number to show how spread out the subjects are in a numerical distribution. (Approximately the average distance between everything and the mean.)

Median times: PG: 101 mins, G: 79 mins

Mean times: PG: 98.1 mins, G: 80.2 mins

SD times: PG: 9.79 mins, G: 7.71 mins

ACTIVITY

Could the difference we see between G and PG films just be random?

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Shuffle your cards well and deal out 17 in one pile and the remaining 35 in a second pile.

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Create two separate histograms for running time for your two new groups.

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Compare to how it turned out for G and PG films.

Terminology

TEST STATISTIC: A number you calculate from the data to help decide a yes-or-no question about a specific number or relationship. �P-VALUE: A probability you calculate from the test statistic to compare your data to what could have been if a specific yes-or-no answer were true.

SIGNIFICANT: The p-value is low (under 0.05), so there is evidence to suggest a difference or relationship is there (but it’s not the same as important and it can’t show cause).

“There is a significant difference in run time on average between G and PG Disney films (t(26)=6.69, p<0.0001)”

ACTIVITY

Organise your cards to investigate the relationship between year of release and running time.

Terminology

SCATTERPLOT: A graph where each subject is a dot lining up with a number on two different axes.

Terminology

CORRELATION COEFFICIENT: A number to say how close to being a straight-line relationship something is. Closer to 1.00 is a stronger relationship.

SIGNIFICANT: The p-value is low (under 0.05), so there is evidence to suggest a difference or relationship is there (but it’s not the same as important and it can’t show cause).

“There is a significant linear relationship between year of release and running time for Disney films (r = 0.685 , t(50)=6.65, p<0.0001)”

ACTIVITY

Investigate whatever you like with the cards. You might like to choose a couple of variables and arrange the cards to see how they are related.

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When you’re happy with your arrangement, have a look at what the other groups have done.

ACTIVITY

Choose something you want to remember.